{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 代表的な離散型確率分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.526093Z",
     "start_time": "2018-08-11T04:29:52.243215Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "%precision 3\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.564269Z",
     "start_time": "2018-08-11T04:29:52.527251Z"
    }
   },
   "outputs": [],
   "source": [
    "# グラフの線の種類\n",
    "linestyles = ['-', '--', ':']\n",
    "\n",
    "def E(X, g=lambda x: x):\n",
    "    x_set, f = X\n",
    "    return np.sum([g(x_k) * f(x_k) for x_k in x_set])\n",
    "\n",
    "def V(X, g=lambda x: x):\n",
    "    x_set, f = X\n",
    "    mean = E(X, g)\n",
    "    return np.sum([(g(x_k)-mean)**2 * f(x_k) for x_k in x_set])\n",
    "\n",
    "def check_prob(X):\n",
    "    x_set, f = X\n",
    "    prob = np.array([f(x_k) for x_k in x_set])\n",
    "    assert np.all(prob >= 0), '負の確率があります'\n",
    "    prob_sum = np.round(np.sum(prob), 6)\n",
    "    assert prob_sum == 1, f'確率の和が{prob_sum}になりました'\n",
    "    print(f'期待値は{E(X):.4}')\n",
    "    print(f'分散は{(V(X)):.4}')\n",
    "\n",
    "def plot_prob(X):\n",
    "    x_set, f = X\n",
    "    prob = np.array([f(x_k) for x_k in x_set])\n",
    "    \n",
    "    fig = plt.figure(figsize=(10, 6))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.bar(x_set, prob, label='prob')\n",
    "    ax.vlines(E(X), 0, 1, label='mean')\n",
    "    ax.set_xticks(np.append(x_set, E(X)))\n",
    "    ax.set_ylim(0, prob.max()*1.2)\n",
    "    ax.legend()\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ベルヌーイ分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.569321Z",
     "start_time": "2018-08-11T04:29:52.565434Z"
    }
   },
   "outputs": [],
   "source": [
    "def Bern(p):\n",
    "    x_set = np.array([0, 1])\n",
    "    def f(x):\n",
    "        if x in x_set:\n",
    "            return p ** x * (1-p) ** (1-x)\n",
    "        else:\n",
    "            return 0\n",
    "    return x_set, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.573425Z",
     "start_time": "2018-08-11T04:29:52.570272Z"
    }
   },
   "outputs": [],
   "source": [
    "p = 0.3\n",
    "X = Bern(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.577547Z",
     "start_time": "2018-08-11T04:29:52.574372Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は0.3\n",
      "分散は0.21\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.655382Z",
     "start_time": "2018-08-11T04:29:52.578567Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.659593Z",
     "start_time": "2018-08-11T04:29:52.656761Z"
    }
   },
   "outputs": [],
   "source": [
    "rv = stats.bernoulli(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.664760Z",
     "start_time": "2018-08-11T04:29:52.660932Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.700, 0.300)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.pmf(0), rv.pmf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.670243Z",
     "start_time": "2018-08-11T04:29:52.666156Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.7,  0.3])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.pmf([0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.676172Z",
     "start_time": "2018-08-11T04:29:52.671550Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.7,  1. ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.cdf([0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.680896Z",
     "start_time": "2018-08-11T04:29:52.677529Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.300, 0.210)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.mean(), rv.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二項分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.688424Z",
     "start_time": "2018-08-11T04:29:52.682189Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.special import comb\n",
    "\n",
    "def Bin(n, p):\n",
    "    x_set = np.arange(n+1)\n",
    "    def f(x):\n",
    "        if x in x_set:\n",
    "            return comb(n, x) * p**x * (1-p)**(n-x)\n",
    "        else:\n",
    "            return 0\n",
    "    return x_set, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.692070Z",
     "start_time": "2018-08-11T04:29:52.689659Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "p = 0.3\n",
    "X = Bin(n, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.696902Z",
     "start_time": "2018-08-11T04:29:52.693401Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は3.0\n",
      "分散は2.1\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.816191Z",
     "start_time": "2018-08-11T04:29:52.698235Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.923246Z",
     "start_time": "2018-08-11T04:29:52.817283Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "x_set = np.arange(n+1)\n",
    "for p, ls in zip([0.3, 0.5, 0.7], linestyles):\n",
    "    rv = stats.binom(n, p)\n",
    "    ax.plot(x_set, rv.pmf(x_set),\n",
    "            label=f'p:{p}', ls=ls, color='gray')\n",
    "ax.set_xticks(x_set)\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 幾何分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.928098Z",
     "start_time": "2018-08-11T04:29:52.924337Z"
    }
   },
   "outputs": [],
   "source": [
    "def Ge(p):\n",
    "    x_set = np.arange(1, 30)\n",
    "    def f(x):\n",
    "        if x in x_set:\n",
    "            return p * (1-p) ** (x-1)\n",
    "        else:\n",
    "            return 0\n",
    "    return x_set, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.932565Z",
     "start_time": "2018-08-11T04:29:52.929113Z"
    }
   },
   "outputs": [],
   "source": [
    "p = 0.5\n",
    "X = Ge(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:52.937365Z",
     "start_time": "2018-08-11T04:29:52.933564Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は2.0\n",
      "分散は2.0\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.147060Z",
     "start_time": "2018-08-11T04:29:52.938358Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAFoCAYAAAB+Cg5cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAG5BJREFUeJzt3W2QneV9HvDrT0S02DCQ4GAPUhsxsvNiB2xgMXJNLFEbxynpmDjpiyd12qZUcZx+yKR50UxnGoZJajqux5N03LjCSePUjT+kwXYcQmNCkBvVCCPANm/jmJeFyMRv61Z2iIUR3P2wKwKHI/bss/eRzsLvN6OZfaT7/Pc6q1tnLz3n2XOqtRYAANbmhOMdAADguUCpAgDoQKkCAOhAqQIA6ECpAgDoQKkCAOhgxVJVS66uqtuq6spnWfcbVfWpqtrdNyIAwOyb5EzVtiRzSeaT7KyqM0cXVNVrkxxsrb166bBe0TcmAMBsm6RUnZ/kxiTnJNmb5Nwxay5JcmJV/VmSh1trd/WLCAAw+yYpVacm+WqSM5LsWT4e9ZIkc621v5/k+6vqgm4JAQDWgQ0TrDmYZGOSu7N01uqBMWv+OktnsZLkE0lenuSWpy6oqp1JdibJC17wgvO3bt06MHIfhw8fzoYNk9z98e6///488cQTeelLX3rcs/SaMWtzZilLrzmyTHeOLNOdI8t058xSll5zZinLWtxxxx1fba1914oLW2vP+ivJa5L8p+WPr0ty5pg1P57kncsf/1aSbc828/zzz2/H2wMPPLCm22/fvr2dd955M5Gl14xZmzNLWXrNkWW6c2SZ7hxZpjtnlrL0mjNLWdYiyf62Ql9qrU309N++JKdV1c1JbmmtPTxmzUeSbK6qTyb5f621fRPMBQB4zljxXNpyQ7v8yHFVbU9yQ5KtrbUHl9ccTvK2aYUEAJh1Q178c3+SVyUZd8YKAOB5adVXfbXWHkly5xSyAAAz7rHHHsuBAwdy6NChFdcePnw499xzz5o/Z685K5mbm8vmzZtz4oknDrr98buUHgBYdw4cOJBTTjklW7ZsSVU969pHH300GzduXPPn7DXn2bTWsri4mAMHDuSss84aNMN7/wEAEzt06FBOP/30FQvVelNVOf300yc6A3c0ShUAsCrPtUJ1xFrvl1IFANCBUgUA0IEL1QGAdeWKK67IZz/72Xzzm9/MF7/4xfzSL/1SPvvZz+bmm2/OySefnA996EN5wQtekJ/4iZ/Ifffdl+/7vu/LBz7wgezZsye/+7u/my9/+cv52te+lmuvvTbf8R3f0S2XUgUADLZjx46j/tkTTzyRE05Y3ZNie/bsmWjd2972tvzqr/5q3vWud+Xd7353Pv/5z2fz5s05cOBAPvnJT2br1q257rrrcu655+a6667Ll770pSTJQw89lI9//ON55zvfmRtvvDFvectbVpXv2Xj6DwBYd0466aSccsop2bBhQx544IG84x3vyJ49e3LbbbflkksuyeLiYi666KJce+212bFjR775zW8mSebn53PCCSfk9NNPz9e//vWumZypAgAGe7YzS8fi9aWSZNOmTdm3b+lth9/znvfkwgsvzBe+8IW89rWvzeHDh/OpT31q6hkSZ6oAgHXuggsuyBlnnJGLL744t99+e7Zt25aLL744H/zgB/PWt741b3jDG/L+979/6jmcqQIA1pUrrrgiSfKmN70pyfjrul70ohflzjuf+a56R9a+/e1v757LmSoAgA6UKgCADpQqAIAOlCoAgA6UKgCADpQqAIAOlCoA4Hlhz5492bVr19Tme50qAGCwLbuu7Tpv4apL13T7b33rW0mSb//2b+8RZ1WUKgBgXdmzZ08++MEPZmFhId/2bd+Wj370o7nqqqty4okn5kMf+lBuuOGGvPjFL87P/uzP5rbbbsvZZ5+d3bt3J0n279+fSy65JK21fOxjH8tJJ53ULZen/wCAdef+++/P9ddfn4suuigf/vCHkyTXX3999u7dmxe/+MW55ZZb8jd/8ze56aabcsIJJ2Tv3r1Jkg0bNuT666/PxRdfnGuuuaZrJqUKAFh35ufnU1V55StfmQcffDBJsmvXrpx22mlJkvvuuy/nnXdekuS8887L5z//+Sc/TpKzzz47Dz/8cNdMShUAsO7cdNNNSZI77rgjZ5111jP+fOvWrbn99tuTJJ/5zGeeXLN///4kyac//em87GUv65pJqQIA1p3WWrZv3559+/blsssue8afX3DBBTnppJPy6le/Ot/4xjeyffv2JMmZZ56Z17/+9dmzZ8+Tb8jciwvVAYB156KLLspVV1315PEVV1zxjDXvfe97n3a8Y8eO7NixY2qZlCoAYLBnewmERx99NBs3bjyGaY4vpQoAWFemfcZpKNdUAQB0oFQBAKvSWjveEaZirfdLqQIAJjY3N5fFxcXnXLFqrWVxcTFzc3ODZ7imCgCY2ObNm3PgwIF85StfWXHt4cOHs2HD2qtGrzkrmZuby+bNmwffXqkCACZ24oknjn2xzXEWFhayZcuWNX/OXnOmzdN/AAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdrFiqasnVVXVbVV15lDWXVtVfVNXe5V8n948KADC7NkywZluSuSTzSR6uqve11h4eWXNykv/QWvudzvkAANaFSZ7+Oz/JjUnOSbI3yblj1pyc5Keq6pNV9f6O+QAA1oVJzlSdmuShJGck2bN8POrBJL/eWvuDqvpAVf1ga+3Pn7qgqnYm2ZkkmzZtysLCwlpyT2TH++5aYcX4P9/z9lesOPvQoUN5/PHHu9yPxcXFmZgxa3NmKUuvObJMd44s050jy3TnzFKWXnNmKcuxMEmpOphkY5K7s3TW6oHRBa21P33K4c1Jtib585E1u5PsTpL5+fm2ZcuWYYlXZaVSNd4k2ebm5vLYY49NtLbX5zwWM2Ztzixl6TVHlunOkWW6c2SZ7pxZytJrzixlmbZJnv67NcmFrbV7k7wuye2jC6rql6vq0uXDbUk+1y8iAMDsm6RU7UtyWlXdnOSWMRepJ8lvJ/n5qtqf5GBr7aaeIQEAZt2KT/+11lqSy48cV9X2JDck2dpae3B5zVeSvH5aIQEAZt2QF//cn+RVScadsQIAeF6a5EL1p2mtPZLkzilkAQBYt7xNDQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHK5aqWnJ1Vd1WVVeusPYXqmpfv3gAAOvDJGeqtiWZSzKfZGdVnTluUVW9Isn3dswGALBuTFKqzk9yY5JzkuxNcu7ogqo6McmvJfmFrukAANaJDROsOTXJQ0nOSLJn+XjUv0/y6621g1U1dkhV7UyyM0k2bdqUhYWFAXGPjUmyHTp0KI8//niX+7G4uDgTM2Ztzixl6TVHlunOkWW6c2SZ7pxZytJrzixlORYmKVUHk2xMcneWzlo9MGbNDyf5war6lSQvr6pfbK2966kLWmu7k+xOkvn5+bZly5a15J7QXYNuNUm2ubm5PPbYYxOt7fU5j8WMWZszS1l6zZFlunNkme4cWaY7Z5ay9JozS1mmbZKn/25NcmFr7d4kr0ty++iC1tp8a21Ha21HkrtHCxUAwHPdJKVqX5LTqurmJLe01h6eciYAgHVnxaf/WmstyeVHjqtqe5IbkmxtrT04Zv22rgkBANaBIS/+uT/Jq5I4YwUAsGySC9WfprX2SJI7p5AFAGDd8jY1AAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB2sWKpqydVVdVtVXXmUNZur6saq2ltVH62qF/aPCgAwuyY5U7UtyVyS+SQ7q+rMMWtemOTy1tpFSb6c5Af6RQQAmH2TlKrzk9yY5Jwke5OcO7qgtfa5JJur6s4kL2yt3dw1JQDAjJukVJ2a5KtJzkiyZ/n4GVprn0hydpJHqmpbr4AAAOvBhgnWHEyyMcndWTpr9cDogqr6/iQHWmvfqKo/TrI9yb6RNTuT7EySTZs2ZWFhYW3Jp2iSbIcOHcrjjz/e5X4sLi7OxIxZmzNLWXrNkWW6c2SZ7hxZpjtnlrL0mjNLWY6FSUrVrUl+rLX2+1X1uiQfGLPmzUm+lOS/JTkvyR2jC1pru5PsTpL5+fm2ZcuWoZlX4a5Bt5ok29zcXB577LGJ1vb6nMdixqzNmaUsvebIMt05skx3jizTnTNLWXrNmaUs0zbJ03/7kpxWVTcnuaW19vCYNb+Z5M1V9edJNie5pmNGAICZt+KZqtZaS3L5keOq2p7khiRbW2sPLq85mOSyaYUEAJh1Q178c3+SVyUZd8YKAOB5aZJrqp6mtfZIkjunkAUAYN3yNjUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdbDjeAWbdll3Xjv39L96/+Kx/vnDVpVPLBADMHmeqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpQqgAAOlCqAAA6UKoAADpYsVTVkqur6raquvIoa76zqj5WVTdV1W9VVfWPCgAwuyY5U7UtyVyS+SQ7q+rMMWvekeS/t9Zek+S0JGf3iwgAMPs2TLDm/CQ3Jjknyd4k5yZ5eGTNDUnuWf74W0n+b6+AAADrwSSl6tQkDyU5I8me5eOnaa3dlCRV9Y4k97TW/nJ0TVXtTLIzSTZt2pSFhYXBoaetR7bVzFhcXFzz5+sxY9bmzFKWXnNkme4cWaY7R5bpzpmlLL3mzFKWY2GSUnUwycYkd2fprNUD4xZV1a4kj7bWxl531VrbnWR3kszPz7ctW7YMybtKdw261dOz9ZjRf/20ZszanFnK0muOLNOdI8t058gy3TmzlKXXnFnKMm2TXFN1a5ILW2v3JnldkttHF1TVa5L83dbaezrnAwBYFyYpVfuSnFZVNye5pbU2ej1VkvxMku1VtXf51xu7pgQAmHErPv3XWmtJLj9yXFXbs3Rh+tbW2oPLa35yagkBANaBIS/+uT/Jq/LMnwAEAHjemuRC9adprT2S5M4pZAEAWLe8TQ0AQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAdKFQBAB0oVAEAHShUAQAcbjneA54stu65dYcVdY3934apL+4cBALpzpgoAoAOlCgCgA6UKAKADpQoAoAOlCgCgA6UKAKADpQoAoAOlCgCgA6UKAKCDFUtVLbm6qm6rqiufZd3PVdV9feMBAKwPk5yp2pZkLsl8kp1VdeZR1i0k+WqnXAAA68okper8JDcmOSfJ3iTnjlvUWvtIktYvGgDA+jHJGyqfmuShJGck2bN8vGpVtTPJziTZtGlTFhYWhow5Jnpk63X/Jp2zuLjY5fPN0pxZytJrjizTnSPLdOfIMt05s5Sl15xZynIsTFKqDibZmOTuLJ21emDIJ2qt7U6yO0nm5+fbli1bhoxZpbsG3erp2XrM6Dmnz9r1MmeWsvSaI8t058gy3TmyTHfOLGXpNWeWskzbJE//3ZrkwtbavUlel+T26UYCAFh/JilV+5KcVlU3J7mltfbwlDMBAKw7Kz7911prSS4/clxV25PckGRra+3BkbXbuicEAFgHhrz45/4kr0rijBUAwLJJLlR/mtbaI0nunEIWAIB1y9vUAAB0oFQBAHSgVAEAdKBUAQB0oFQBAHSgVAEAdKBUAQB0oFQBAHSgVAEAdKBUAQB0oFQBAHSgVAEAdKBUAQB0oFQBAHSw4XgHYHJbdl27woq7xv7uwlWX9g8DADyNM1UAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB0oVQAAHShVAAAdKFUAAB1sON4BOPa27Lp2hRV3jf3dhasu7R8GAJ4jnKkCAOhAqQIA6ECpAgDoQKkCAOhAqQIA6ECpAgDoQKkCAOjA61QxmNe7AoC/5UwVAEAHShUAQAdKFQBAB0oVAEAHLlTnuHKxOwDPFSueqaolV1fVbVV15VHWbKyqD1fV7VX10/1jAgDMtknOVG1LMpdkPsnDVfW+1trDI2vekuTOJP8iyf1V9TuttUe7JoVn4YwXAMfbJKXq/CQ3Jjknyd4k5yYZLVXnJ/njLBWwfUlemqN9F4MZtXIxSyYpZwoewPNTtdaefUHVv0tyR5JDSb4nyddaa783subqJP85yUuSvDHJNa21T46s2Zlk5/Lh9yb5XI87sAYvSvLVNc44K8kDM5Klx4xZmzNLWXrNkWW6c2SZ7hxZpjtnlrL0mjNLWdbiu1tr37XSoknOVB1MsjHJ3Vk6IzWuRBzM0h3+TJIfWz5+mtba7iS7J/h8x0RV7W+tza9xxiNrndExy5pnzNqcWcrSa44s050jy3TnyDLdObOUpdecWcpyLEzykgq3JrmwtXZvktcluf0oa16e5CtZeprw3m4JAQDWgUlK1b4kp1XVzUluGXORepJ8OMnrl9e6SB0AeN5Z8em/tnTR1eVHjqtqe5IbkmxtrT24vOZQkh+dVsgp6fFU5DUdZiR9svR6anWW5sxSll5zZJnuHFmmO0eW6c6ZpSy95sxSlqlb8UL1Z9yg6oVZukD7c621x6aSCgBgnVl1qQIA4Jmed+/9V1VvraqvVtXcGmacUlULVXWwqr5YVacMnHNyVf1xVe2tqhuq6iVryPTjVfVXa7j9K6rqoeUse6vqpWuYtauqbll+lf1VvxVSVf3UU3LcW1W/PDDHxqr6H8tzrquqFw+cc1JV/X5V7amq967ytk/ut0nenWCSOeOOB+bZWFW/t/z1+cOq2jhgxuA9PO4+rHYfj2QZvIfHfH0H7eGRPIP28Zi/o0F7eGTOoD08bo+sdg8fZcaq9+9R5qxq/465zalD9u/RPveA/Ts655Wr3cNH+bqsev+OmfPTA/fvuDyr2sNH+Xsa9Bh8rD3vSlWSb2Ttr5H1H5Pc1Vo7NcmBJIO+6Sc5Lcmu1tpFSf4syfYhQ5YfCN6a5C8H5kiSk5P8dmvtouVfg36Cs6o2J/n+1toFSW5LcslqZ7TWnsyR5JNJ/nBIliRvSPKXy3NuTvKDA+e8Lcn/aq3tSHKoqv7eKm771P321Hcn2FlVZw6cM+54yJx/lOTTy1+fzyf5oQEz1rKHn3YfBu7jp85Yyx5+cs4a9/CTc9awj596n9ayh586Z+geHt0ju7L6PTxunw3Zv6Nz/smYuaud8eYM27/PuE8D9+/onMuy+j087usyZP+Ozvmrgft3dM6bsvo9PDrjn2f4Y/Ax9bwrVa21P0qy1mvB/jTJryx/fDjJQwOzHEjyaFXdmqWNP/TC93cn+fkkTwy8fbL0DemHq+r/VNVHJvlf31G8IcnBqvp4kk1J/mRooKo6Ocnfaa3dM3DEQpKfq6rPZekf9kcGzjkhyZH/XZ2e5LxJbziy38a9O8GQOYP38cjtPpPkyAv5Hs6EL6z31Blr2cNj7sOq9/HIjMF7eGTO4D087u9ltft4ZMZCBu7hkTlD9/DoHmlZ/R5+xj4buH9H5zw4OnfAjHszbP+O+7cz5HF4dM7hrH4Pj87YnGH7d+zjwYDH4XFzVruHR2ecnIGPwcfa865U9dBau6a1tr+q3pnklOUXNh0663OttSPfbFf9E5RV9a+TfPzIT2KuwVez9HIYr83Shv7HA+e8JEv/AN+Y5OtZejHYoX48a/sJy79K8qOtte9N8tEsvTflEB9I8rKq+pMs/Q970NO9SU7N0tf5jCR7lo+Pm9baHa21A1V1WZJTR98FYRVz1rSHk277eBb3cLK2fXxc9/DoHknyeFa5hzvus9E5n1jt3HFZhuzfMV+XV2TA/h0z54+yyj08ZsYTGbB/n+XvaVX7d0yee7LKPTxmxnvS5zF46pSqgarqv2Tpf7Q/sIYZZ1XVkZe9/8MkFw8Y8+Yk/7Kq9iR5eVW9e0iW1tpnWmu/uXx4c5KtQ+Yk+eskn1j++BNZelHYof5p1laqfjFL35SSpf8dvXbgnG8luby19kNZesumxYFzjrw7wf1ZelB4xjsPHGtV9c+SXJTkZwbevsceTjrs4xndw8na9vFx38Mje2TQHl7rPjvanCFzn3qbtezfkc89eP8+dc7QPTySZfD+PcrXc9X7d2TOoD08MqPXY/DUKVUDLD+fe1lr7YK2th+fvDDJv1n++LwMeB/B1tqPtNZ2LD/XfHdr7d8OCVJLF46+fflwW4Zfd3ZTlu5XsnSfBs2pqlOTnN5a+8LAHEccee79NUnuGzhjR5JfW/74R7J0fcEQk7w7wTFTVd+d5Mdaa7+whn285j2c9NnHs7aHlzP12MfHbQ+P2SOr3sOd9tkz5gyZO+Y2g/bv6Jyh+3fMfVr1Hh5znwbt33FfzyH79yh/L6vaw2Nm7Eifx+CpU6qGeWeSF9XST/8drKr/OnDOHyQ5q6r+d5Y2yvu6JVy9Dyf5B1W1L0tveP37Q4a01m5N8nBV3ZTkpUn+58A8P5KlF5ldi/ckectyln+Y5DcGzrkxyXcuz/mL1tqdA+dM8u4Ex9K/SnJ2/e1P+PzkgBn28LNb6z4+3nv4aXskyfdk9Xu4xz4bl+XGAXNHZ2zMsP07rft0Yla/h0dnvCLD9u+4+zRk/47muSer38OjMzalz2Pw1HmdKgCADpypAgDoQKkCAOhAqQIA6ECpAgDoQKkCAOhAqQIA6ECpAgDoQKkCAOjg/wPG8OuMBSGSKQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.283740Z",
     "start_time": "2018-08-11T04:29:53.148140Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "x_set = np.arange(1, 15)\n",
    "for p, ls in zip([0.2, 0.5, 0.8], linestyles):\n",
    "    rv = stats.geom(p)\n",
    "    ax.plot(x_set, rv.pmf(x_set),\n",
    "            label=f'p:{p}', ls=ls, color='gray')\n",
    "ax.set_xticks(x_set)\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ポアソン分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.289297Z",
     "start_time": "2018-08-11T04:29:53.284830Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.special import factorial\n",
    "\n",
    "def Poi(lam):\n",
    "    x_set = np.arange(20)\n",
    "    def f(x):\n",
    "        if x in x_set:\n",
    "            return np.power(lam, x) / factorial(x) * np.exp(-lam)\n",
    "        else:\n",
    "            return 0\n",
    "    return x_set, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.295486Z",
     "start_time": "2018-08-11T04:29:53.290292Z"
    }
   },
   "outputs": [],
   "source": [
    "lam = 3\n",
    "X = Poi(lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.302299Z",
     "start_time": "2018-08-11T04:29:53.296503Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は3.0\n",
      "分散は3.0\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.451672Z",
     "start_time": "2018-08-11T04:29:53.303359Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dCFoAAJ0IWgAAnQhaAACdCFoAAJ0IWgAAnQhaAACdCFoAAJ0IWgAAnQhaAACdLBm0auDTVXVbVV32Mu1+raoenLe9pqquqarbq+p9o+owAMBKMcyK1oYka5NMJ9lSVSfuo91MksfnbV+Y5O4km5N8pKrWLL+bAAArz+oh2rw5yY1JTk2yI8lpSR5b2Ki19vmq2rpgvz/LIKjtTPLaJPccaIfhQExt3bYfrZf+dp25/ILldwaAiTdM0Do6yVeTHJ9k+9z2MI7OYIXr1UnuXWy/qtqSZEuSrFu3LjMzM0Meur/Z2dmD3YUXGcd7M67331gGxvU9Nkl1Jmks46pjLId3HWM5+IYJWk8kWZPkyxmsUj085LGfSHJckjuSXDS3/SKttSuSXJEk09PTbWpqashDj8fy+zP6hbvF+zLaOuOoMa46+/7ajavOePY/HOtM0ljGVcdYDu86xnJwDXON1q1JzmytPZDk7CS3D3nsW5O8Mcm3Mzjt+MCyeggAsEINE7R2JjmmqnYluaW19pLrs/bhmiTnzu1/ZWvt2WX2EQBgRVry1GFrrSW5eO92VW1KckOS9a21Rxa03TDv82eSvHt0XQUAWFmWc8PS3UnelEX+8hAAgH8wzMXwL9JaeyqD+2MBAPAyPIIHAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoBNBCwCgE0ELAKATQQsAoJMlg1YNfLqqbquqy/bRZk1VXVNVt1fV++Ze+2BV3VVVO6rq2lF3HADgULd6iDYbkqxNMp3ksar6VGvtsQVtLkxyd5JfTPJQVV2Z5Kgkv9pa2z6y3gIArCDDnDp8c5Ibk5yaZEeS016mzYYkO5O8NoOg9e+r6otV9Vuj6S4AwMoxTNA6OsnjSY5Psn1ue19tWpJ757bvTfIfW2tvSXJ2Vb1mFB0GAFgphjl1+ESSNUm+nMHK1cP7aHNckjuSXJTkidbaH87791uSnJzkkfk7VdWWJFuSZN26dZmZmdnP7u+fzZ+6Zz/3WLr99vf/xPI6s596vzfjqjGuOgdzLPv3fTZc2wP5PpudnV32vodanUkay7jqGMvhXcdYDr5hgtatSS5qrV1dVWcnuWofbd6YwYrXqUkeqKr/muS/ZfA/yXSS31m4U2vtiiRXJMn09HSbmppaxhD2x/4GraUt3ueVWWfyxzKuOuN6z8a3/6FUZ5LGMq46xnJ41zGWg2uYU4c7kxxTVbuS3LLIhfBJck2Sc+faXtlaezbJf0nyyQxC2F+01r4+oj4DAKwIS65otdZakov3blfVpiQ3JFnfWntkrs0zSd69YL/7kmwcaW8BAFaQ5dywdHeSNyVZbGULAIA5w1yj9SKttacyuGcWAAAvwyN4AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADoRtAAAOhG0AAA6EbQAADpZfbA7ACzP1NZt+9H6niVbzFx+wfI7A8CirGgBAHQiaAEAdCJoAQB0ImgBAHQiaAEAdCJoAQB0ImgBAHQiaAEAdCJoAQB0ImgBAHQiaAEAdCJoAQB0ImgBAHQiaAEAdCJoAQB0svpgdwA4dE1t3bafe9yzZIuZyy9YXmcAViArWgAAnQhaAACdCFoAAJ0IWgAAnQhaAACdLBm0auDTVXVbVV22jzZrquqaqrq9qt4399qrquqGqvpSVf3MqDsOAHCoG+b2DhuSrE0yneSxqvpUa+2xBW0uTHJ3kl9M8lBVXZnkfUn+MMmuJH+c5E9H1GdgwuzfbSSWvoVE4jYSwKFhmFOHb05yY5JTk+xIctrLtNmQZGeS18577Y1JvlNVPzSKDgMArBTDrGgdneSrSY5Psn1ue7E2jyd5dZJ757b3vvbdJI/NbT91wD0GWKZRr5xZNQOWUq21l29Q9StJvpnk9iQ/l+TO1tq2BW3+U5I/y2BmuizJf07yW0k+nOT/Jfl8kgtba08t2G9Lki1zmz+e5L4DHM8oHZdBUFzpNcZZ5+QkD3euMUnv2SSNZVx1Jmks46pjLId3HWPp5zWttR9ZqtEwK1q3JrmotXZ1VZ2d5Kp9tHljBitepyZ5YO61dUm+kuSVC0NWkrTWrkhyxRB9GLuq2t1am17pNcZc5ynv2aFVY9LqTNJYxlXHWA7vOsZy8A1zjdbOJMdU1a4ktyxyIXySXJPk3Lm2V7bWns0gQP2rDMLXR0fTXQCAlWPJFa02OLd48d7tqtqU5IYk61trj8y1eSbJuxfsN5tB+AIAOCwt54alu5O8KYML3CfZOE5pjuu06bjqfG4MNSbpPZuksYyrziSNZVx1jOXwrmMsB9mSF8MDALA8HsEDANCJoLXAMI8cGlGd91TV41W1tmONNVX1h1W1o6r+pKrWdKhxQlV9q6qeqKrvVNUpo66xoN7PVtVfdzz+T1TVV+fesx1V9dpOdbZW1S1zj64a5q9/l1Pjl+aN44Gq+s1OddZU1X+fq3NtVZ3QocaRVXV1VW2vqk90OP4LP48954CFP/c95oEFY+k2Byyoc1RV/dlcnRuq6tU96sx7baTzwIKxdJsDFvn6j3weWDCWbnPAIt9nXeaABXW6zgO9CFovNf+RQ1uq6sROdZ5M//uG/VySL7XWNia5P8nbO9T40SQfaK0dncH1e7/coUaSZG7yfk+Sr/WqkeSoJL/XWts49/HAqAtU1UlJ3tBaOyPJbUnOH3WNJGmtvTCOJDcl+ZMedZKcl+Rrc3V2JXlbhxrvTfLnrbXNSZ6pqp8a8fHn/zz2nAMW/tz3mAfmH7PnHDC/zjFJts7V+d9JNnWq02semF+j5xzwQp2O88ALNTrPAfPfs55zwPw6veeBLgStlxrmkUMHrLX2v5J8v8ex57kjg+dNJsmedLjRW2ttd5KnquqpJG9J8u9GXWOejyX59STPd6xxVJJ/VFX/t6o+32MVMINJ6Ymqui6De839RYcaL6iqo5L8aGvt3k4lZpL8WlXdl+QdGdygeNRWJdn7W/KxSU4f5cEX/Dx2mwMW/tz3mAcWHLPbHDC/Tmvt0STPVtWtGQSGkf1hzCLv0cjngQU1us0BC+p0mQcW+57qMQcsqDOTTnPAgjpd54FeBK2X2vvooJd75NCK0Fq7q7X2aFW9K8nRrbWbOtX589baD2XwW9lHetSoqn+Z5Lq9txTp6PEM7gX31gz+k/qnHWq8OoNJ76eTfC/JRR1qzPez6fsXoX+d5N2ttR9P8j8zeLj8qF2V5HVV9RcZ/Ib7yg419jIHLK/Wfa21vSH13Uu1X44xzQPjmAOS8c4DkzAHJOOdB0ZG0HqpJ5KsSfJQBl/EJw5udw5MVf3zJBuTfKDT8d9WVa+f27winU6DJfknSf5FVW1P8saq+liPIq21O1prn5zb3JVkfYcyf5vkC3OffyGDpyr09M/Sd5L9txlMtMngN9m3dqjxXJKLW2tvT3JXktkONfYyB+x/jZOrau+jSP4kyTmdSnWfB8Y0ByTjnQcmYQ5IxjsPjIyg9VK3Jjlz7rz82Rk843FFqqrXZPD4pH/T+t3H42eTfGru87cn6fKbZmvtna21zXPn5r/cWvvXPerMXXj5/rnNDelzHd3NSc6c+/z0TjWSJFV1dJJjW2tf71Vjzt5rJc5K8mCH42/O4NmpSfLODK436cUcsP/OTPIrc5+fnk7PPB3HPDCmOSAZ0zwwQXNAMt55YGQErZca5pFDK8UvJzll3l+d/EKHGluT/GhV/U0GQWvLEu0Pddck+cdVtTODB51fPeoCrbVbkzxWVTcneW2SPx51jXnemcGTHHr6eJIL58bzMxk8VH7UbkzyqrkaX2mt3d2hxl7mgP33P5KcXFX/J4PvuU8t0f5Q1n0OSMY6D0zKHJCMdx4YGTcsBQDoxIoWAEAnghYAQCeCFgBAJ4IWAEAnghYAQCeCFgBAJ4IWAEAnghYAQCf/H8T7qpTYfeBOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T04:29:53.580909Z",
     "start_time": "2018-08-11T04:29:53.453029Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "x_set = np.arange(20)\n",
    "for lam, ls in zip([3, 5, 8], linestyles):\n",
    "    rv = stats.poisson(lam)\n",
    "    ax.plot(x_set, rv.pmf(x_set),\n",
    "            label=f'lam:{lam}', ls=ls, color='gray')\n",
    "ax.set_xticks(x_set)\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
